Further results concerning the refined theory of anisotropic laminated composite plates

Abstract

A simple refined discrete-layer theory of anisotropic laminated composite plates is substantiated. The theory is based on the assumption of a piecewise linear variation of the in-plane displacement components and of the constancy of the transverse displacement throughout the thickness of the laminate. This plate model incorporates transverse shear deformation, dynamic and thermal effects as well as the geometrical non-linearities and fulfills the continuity conditions for the displacement components and transverse shear stresses at the interfaces between laminae. As it is shown in the paper, the refinement implying the fulfillment of continuity conditions is not accompanied by an increase of the number of independent unknown functions, as implied in the standard first order transverse shear deformation theory. It is also shown that the within the framework of the linearized static counterpart of the theory, several theorems analogous to the ones in the 3-D elasticity theory could be established. These concern the energetic theorems, Betti's reciprocity theorem, the uniqueness theorem for the solutions of boundary-value problems of elastic composite plates, etc. Finally, comparative remarks on the present and standard first order transverse shear deformation theories are made and pertinent conclusions about its usefulness and further developments are outlined.

A Review of Refined Shear Deformation Theories of Isotropic and Anisotropic Laminated Plates

“…In these theories a piecewise linear displacement function is superimposed over a linear displacement field. The theories of Mau [350], Chou and Carleone [351], Durocher and Solecki [352], Di Sciuva [353,354], Murakami [355], He et al [356], Schmidt and Librescu [357], Bisegna and Sacco [358] belong to this catagory. Most of the authors of these theories used the zig-zag functios or the Heaviside unit function to get the kinky, zigzag distribution of inplane displacements through the thikness of laminate since this type of distribution is given by exact elasticity solutions obtained by Pagano [236,237] for thick laminated plates.…”

Dynamic Behaviour of Undamaged and Damaged Multilayered Composite Plates

“…The response of damaged multilayered structures is a topic of main importance because defects, due to manufacturing processes or operating conditions, may lead to an abrupt reduction of the load carrying capacity of the component [1]. Several methods have been proposed to analyse multilayered composite plates with interfacial defects.…”

Stress Fields in Fiber Reinforced Laminate Beams Due to Bending and Torsion Moments

“…These models were improved considering also the warping effect on the overall behavior of the beams through the ''higher-order shear deformation'' theories established by Whitney and Sun [7], Lo et al [8], Reddy [9,10] and Noor and Burton [11]. Librescu and Song [12] as well as Schmidt and Librescu [13] developed a refined theory for composite laminated beams of arbitrary thin-walled closed cross-section taking into account torsionalrelated warping effects. This theory was modified later for open crosssection beams and a number of non-classical effects, such as the transverse shear flexibility and warping restraint, were studied by Song and Librescu [14].…”